Time dilation is the effect that for some objects, more time as passed than for others, depending their position and velocity. It is a consequence of relativity.
Special relativity implies time dilation based upon the relative motion of two objects. General relativity also produces time dilation depending upon how curved space is, which is an aspect of gravity, in which case it is called gravitational time dilation.
Cosmological time dilation is the apparent time dilation of events viewed from large (high redshift) distances.
Time dilation challenges intuition based upon daily experience, but is not only proven, but some technology that depends upon high-precision time measurement, such as GPS, requires time dilation to be taken into account in order to function.